Could the temperature eleven millennium ago been the same as a century ago?

In March 1866 Julius Von Haast made a drawing of the debris-covered Ramsay Glacier 300 m below him1. He was atop Mein’s Knob, a vantage point from which he described the view as “…second to none in New Zealand”.

Haast noted he was standing near glacial moraine remnants which meant that at some previous time the Ramsay glacier must have been 300 m thicker and abutted right up to near the top of Mein’s Knob. He considered this evidence that the Southern Alps had, in the past, been subject to a climate different to what he was experiencing.

From about the same time, New Zealand began a systematic programme of temperature observations. We now know that the climate during Haast’s time was 1oC cooler than now2.

About 150 years later, Tobias (Toby) Koffman and colleagues3 sampled the quartz from the moraines on Mein’s Knob, and found they had been exposed to the atmosphere for 11 600 years. This is a continuation of amazing work being done to date moraines in the Southern Hemisphere and sort out the global extent of climate variations. Dr Koffman’s group applied a computer model to find what climate was required to enable a glacier to deposit moraines on Mein’s Knob. They found that the temperature would need to be 1o less than today. The same temperature as during Haast’s time when the glacier was 300 m lower.

For the same temperature, Koffman and Haast have two different sized glaciers. Is that possible? Is it likely? Is there a plausible explanation?
Was the temperature eleven millenium ago the same as it was a century ago?